Atkin-Lehner |
3- 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117117bb |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
5001216 |
Modular degree for the optimal curve |
Δ |
217055291169329613 = 310 · 711 · 11 · 132 |
Discriminant |
Eigenvalues |
0 3- 2 7+ 11- 13+ -2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-52200174,145163033239] |
[a1,a2,a3,a4,a6] |
Generators |
[277641709:1095648906:68921] |
Generators of the group modulo torsion |
j |
127680722384510660804608/1761798128013 |
j-invariant |
L |
6.151520374928 |
L(r)(E,1)/r! |
Ω |
0.22353934732467 |
Real period |
R |
13.759368096565 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000076593 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39039b1 117117bj1 |
Quadratic twists by: -3 13 |